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Scenario 1: Find the Amount of Payment

Loan Amount (C)

Residual Value (F)

Interest Rate % (R)

Compound Frequency (m)

No. of Payments (N)

Payment Frequency (q)

Monthly Payment (P): 
The primary reason that leasing generally yields lower monthly payments is that although you are still paying the interest based on the full amount of the loan, the capital parts of the payments only have to add up to the difference between the loan and the Residual Value. The following formula calculates the monthly payment and can be reduced to the Advanced Loan Calculator formula when F = 0.
Scenario 2: Find the Interest Rate

Loan Amount (C)

Residual Value (F)

Payment Amount (P)

No. of Payments (N)

Payment Frequency (q)

Compound Frequency (m)

Interest Rate % (R): 
For given C, P and N, one can only solve the following equation for r by numerical means.
Given the rather smooth behavior of this equation, this calculator employs the Newton-Raphson method with an educated initial guess: